Page 141 - Schaum's Outline of Theory and Problems of Signals and Systems

LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS [CHAP. 3

(b)
Fig. 3-1 1

We see that the ROCs in Eqs. (3.59) and (3.60) overlap, and thus,

From Eq. (3.61) we see that X(s) has one zero at s = - 5 and two poles at s = -2 and
s = - 3 and that the ROC is Re(s) > - 2, as sketched in Fig. 3-1 l(a).
(b) From Table 3-1

We see that the ROCs in Eqs. (3.62) and (3.63) overlap, and thus,

From Eq. (3.64) we see that X(s) has no zeros and two poles at s = 2 and s = -3 and
that the ROC is - 3 < Re(s) < 2, as sketched in Fig. 3-1 l(b).
(c) From Table 3-1

1
e-3r~( -t) - - - Re(s) < - 3 (3.66)
s + 3
We see that the ROCs in Eqs. (3.65) and (3.66) do not overlap and that there is no
common ROC; thus, x(t) has no transform X(s).